Question

hazardous waste: following is a list of the number of hazardous waste sites in a sample of states of the united states in a recent year. the list has been sorted into numerical order.
2 3 5 9 9 11 12 12 13 13
14 15 15 16 19 19 20 21 25 26
32 32 38 40 48 49 49 52 86 97
send data to excel
part 1 of 4
find the first and third quartiles of these data.
the first quartile is 12
the third quartile is 38
part 2 of 4
find the median of these data.
median = 19
part 2 / 4
part 3 of 4
find the lower and upper outlier boundaries.
lower outlier boundary is
upper outlier boundary is

Explanation:

Step1: Recall outlier - boundary formula

The lower outlier boundary (LOB) is $Q_1 - 1.5\times IQR$ and the upper outlier boundary (UOB) is $Q_3+1.5\times IQR$, where $IQR = Q_3 - Q_1$. We know $Q_1 = 12$ and $Q_3 = 38$.

Step2: Calculate the inter - quartile range

$IQR=Q_3 - Q_1=38 - 12 = 26$.

Step3: Calculate the lower outlier boundary

$LOB=Q_1-1.5\times IQR=12-1.5\times26=12 - 39=- 27$. Since we are dealing with non - negative data (number of waste sites), we can consider the lower outlier boundary as 0 (in a practical non - negative data context).

Step4: Calculate the upper outlier boundary

$UOB=Q_3 + 1.5\times IQR=38+1.5\times26=38 + 39 = 77$.

Answer:

Lower outlier boundary is 0
Upper outlier boundary is 77